H2SO4 + HNO3 + Na2S = H2O + S + NO + Na2SO4

H_2SO_4 sulfuric acid + HNO_3 nitric acid + Na_2S sodium sulfide ⟶ H_2O water + S mixed sulfur + NO nitric oxide + Na_2SO_4 sodium sulfate

Balance the chemical equation algebraically: H_2SO_4 + HNO_3 + Na_2S ⟶ H_2O + S + NO + Na_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 HNO_3 + c_3 Na_2S ⟶ c_4 H_2O + c_5 S + c_6 NO + c_7 Na_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, N and Na: H: | 2 c_1 + c_2 = 2 c_4 O: | 4 c_1 + 3 c_2 = c_4 + c_6 + 4 c_7 S: | c_1 + c_3 = c_5 + c_7 N: | c_2 = c_6 Na: | 2 c_3 = 2 c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = (3 c_1)/4 + 3/8 c_4 = c_1 + 1/2 c_5 = c_1 c_6 = 1 c_7 = (3 c_1)/4 + 3/8 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 2 c_3 = (3 c_1)/4 + 3/4 c_4 = c_1 + 1 c_5 = c_1 c_6 = 2 c_7 = (3 c_1)/4 + 3/4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 4 c_5 = 3 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 HNO_3 + 3 Na_2S ⟶ 4 H_2O + 3 S + 2 NO + 3 Na_2SO_4

+ + ⟶ + + +

sulfuric acid + nitric acid + sodium sulfide ⟶ water + mixed sulfur + nitric oxide + sodium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + HNO_3 + Na_2S ⟶ H_2O + S + NO + Na_2SO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 3 H_2SO_4 + 2 HNO_3 + 3 Na_2S ⟶ 4 H_2O + 3 S + 2 NO + 3 Na_2SO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 3 | -3 HNO_3 | 2 | -2 Na_2S | 3 | -3 H_2O | 4 | 4 S | 3 | 3 NO | 2 | 2 Na_2SO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) HNO_3 | 2 | -2 | ([HNO3])^(-2) Na_2S | 3 | -3 | ([Na2S])^(-3) H_2O | 4 | 4 | ([H2O])^4 S | 3 | 3 | ([S])^3 NO | 2 | 2 | ([NO])^2 Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2SO4])^(-3) ([HNO3])^(-2) ([Na2S])^(-3) ([H2O])^4 ([S])^3 ([NO])^2 ([Na2SO4])^3 = (([H2O])^4 ([S])^3 ([NO])^2 ([Na2SO4])^3)/(([H2SO4])^3 ([HNO3])^2 ([Na2S])^3)

Construct the rate of reaction expression for: H_2SO_4 + HNO_3 + Na_2S ⟶ H_2O + S + NO + Na_2SO_4 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 3 H_2SO_4 + 2 HNO_3 + 3 Na_2S ⟶ 4 H_2O + 3 S + 2 NO + 3 Na_2SO_4 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 3 | -3 HNO_3 | 2 | -2 Na_2S | 3 | -3 H_2O | 4 | 4 S | 3 | 3 NO | 2 | 2 Na_2SO_4 | 3 | 3 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Na_2S | 3 | -3 | -1/3 (Δ[Na2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/3 (Δ[Na2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/2 (Δ[NO])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | nitric acid | sodium sulfide | water | mixed sulfur | nitric oxide | sodium sulfate formula | H_2SO_4 | HNO_3 | Na_2S | H_2O | S | NO | Na_2SO_4 Hill formula | H_2O_4S | HNO_3 | Na_2S_1 | H_2O | S | NO | Na_2O_4S name | sulfuric acid | nitric acid | sodium sulfide | water | mixed sulfur | nitric oxide | sodium sulfate IUPAC name | sulfuric acid | nitric acid | | water | sulfur | nitric oxide | disodium sulfate